Productivity Uplift ?Net % increase in output vs. one person working manually. Formula:
(total_value_mult - 1) × 100%. This accounts for everything — robot throughput, recovered failures, AND the time the operator loses to supervising robots. At 640%, one operator + robots produces 7.4× what one person does alone. This is the headline number for customers.+640%
vs. manual work (7.4× total value)
Operator Utilization ?What % of the operator's time is spent fixing failures (M/M/1 traffic intensity: ρ = λ/μ). Calculated as:
failure_arrival_rate / service_rate. The remainder (1 - ρ) is available for manual work. Green <70%, yellow 70-cap%, red >cap%.75%
25% manual capacity
Total Value Multiplier ?Total output of one operator station vs. one person working manually. Two components: (1) Robot throughput =
(successful + recovered tasks) / baseline_rate, and (2) Manual capacity = 1 - utilization — work the operator does between fixing failures. Together: robot_throughput + manual_capacity. This is the number that feeds all economic calculations.7.40×
robots: 6.15× + manual: 0.25×
Value Created / Year ?Dollar value of the extra output compared to a single human. Formula:
(total_value_mult - 1) × baseline_worker_value. The "-1" subtracts the operator's own baseline contribution (they'd be working anyway). This is the value the customer gets from adopting the system.$429K
per operator station
ARR Per Station ?Annual Recurring Revenue we collect from one operator station. Formula:
followers × (software_price + hw_service_price). Each follower needs a software license + hardware service contract. This is what the customer pays us per year.$37.5K
software + hw service
Total Annual Cost ?Full annual cost of ownership per station including recurring fees AND amortized hardware. Formula:
ARR + (leader + followers × follower_cost) / amort_years. This is the true cost the customer bears each year — recurring software and service fees plus the annualized capital investment in leader + follower hardware.$59.3K
recurring + amortized HW
Customer ROI ?Value created divided by total annual cost of ownership. Formula:
value_created / (ARR + amortized_hardware). Includes recurring fees (software + HW service) PLUS amortized robot purchase cost. An ROI of 5× means the customer gets $5 of value for every $1 of total cost. Above 3× is compelling, above 5× is a no-brainer.7.2×
value / total annual cost
Payback Period ?How long until the hardware investment pays for itself. The customer pays full hardware cost upfront (leader + followers). Each year they gain
value_created but also pay recurring fees (software + HW service). Payback = hardware_cost / (value_created - ARR). If annual net value is negative, the system never pays back.---
hardware cost / annual net value
Avg Queue Wait ?Average time a failed robot waits in line before the operator gets to it (M/M/1:
ρ / (λ(1-ρ))). When this exceeds ~5 minutes, the system feels broken — robots are sitting idle waiting for help. This grows exponentially as utilization approaches 100%.1.2 min
0.8 avg queue length
Throughput vs. Followers ?Shows how adding more follower robots increases throughput at your current success rate and speed. Purple line = robot output only. Green line = total value (robot output + operator's remaining manual capacity). The green dot marks your current configuration. The lines end where the system becomes unstable (operator can't keep up).
Operator Utilization vs. Followers ?Shows operator workload as you add followers. The red dashed line is your utilization cap. Below the cap, the operator has breathing room. Above it, queue wait times explode due to M/M/1 queuing dynamics — even a few percent past the cap causes dramatically longer waits. This is why we don't push utilization to 100%.
Queue Wait Time vs. Followers ?Average time a failed robot sits idle waiting for the operator. This is the "cliff" chart — wait times stay low then suddenly spike as you approach the operator's capacity. The yellow line at 5 min marks where the system becomes impractical. This non-linear behavior is why queuing theory matters and why we can't just "add more robots."
Annual Value vs. Total Cost by Followers ?Green bars = dollar value created per year (what the customer gains). Purple bars = ARR — recurring software + HW service fees. Orange bars = amortized robot hardware cost (purchase price / amortization years). The total customer cost = purple + orange. The gap between green and (purple + orange) is the customer's surplus — their incentive to buy. Bars disappear past the utilization cap.
Sensitivity Analysis — What Drives Throughput? ?A tornado chart showing how total value changes when you vary each parameter from your current settings. Each bar shows the impact of moving one parameter to a low/high value while holding everything else constant. Red = value lost, Green = value gained. Sorted by total impact — the top bar matters most. Ranges are asymmetric to show realistic pessimistic vs. optimistic scenarios.
All Tiers Comparison ?Compares all four autonomy tiers using your current intervention time, task time, and utilization cap. "Max Followers" is the most robots one operator can manage without exceeding the cap. The highlighted row matches your current success rate and speed settings. Use this to see how the business model scales across tiers — notice how Customer ROI increases at higher tiers.
| Tier | Success | Speed | Max Followers | Utilization | Total Value | $/yr Created | ARR | Total Cost/yr | Customer ROI |
|---|